A spokesman for the pub, the Prince of Wales in Cardiff said that someone had come into the bar and spoken to the manager about the abandoned children.
"Staff located the father who was on the phone, when they told him of people's concern, he finished the call and walked off," the JD Wetherspoon spokesman said.
A witness told The Sun of their horror at seeing the young children on their own in the freezing street.
"I wouldn't leave a toddler for five seconds. I wouldn't leave them alone at all," the unnamed passer-by said, "I couldn't believe these children had been left alone in a buggy. There was a little one in the front and a toddler sat in the back - at one point he was trying to climb out."
"If he'd got out he could have gone anywhere, it is amazing how quickly they go, they would have been off in a flash," the concerned member of the public added.